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divisor of (15! + 13)?

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by thephoenix » Sat Jan 30, 2010 6:09 am
need to do by option

a)15!/15 yes
but 13/15 no
b)15!/14 yes
13/14 no
c)15!/13 yes
13/13 yes

hence c
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by sanju09 » Sat Jan 30, 2010 6:10 am
rahul.s wrote:which of the following integers is a divisor of (15! + 13)?

A) 15
B) 14
C) 13
D) 7
E) 2

OA: C

approach?
All integer choices are a divisor of 15! but 13 is the only divisor of both 15! as well as 13 or that of 15! ± 13.
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by sunil.hubli » Sat Jan 30, 2010 6:11 am
15! = 15*14*13 .....
therefore 15! + 13 can be factorized to 13(15*14*12! + 1), thus 13 is a divisor of 13

I hope that explains it
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by ajith » Sat Jan 30, 2010 6:27 am
rahul.s wrote:which of the following integers is a divisor of (15! + 13)?

A) 15
B) 14
C) 13
D) 7
E) 2

OA: C

approach?
15! = 1*2*..*13*14*15

= 13k (k being 1*2*3....*12*14*15)


15!+13 = 13K +13 = 13(K+1) so 13 is a factor of 15!+13 so C
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